A BOX MODEL FOR NON-ENTRAINING, SUSPENSION-DRIVEN GRAVITY SURGES ON HORIZONTAL SURFACES

The propagation of and the deposition from a turbulent gravity current generated by the release of a finite volume of a dense particle suspe nsion is described by a box model. The approximate model consists of a set of simple equations, a predetermined; depth-dependent leading bou ndary condition and one experimentally determined parameter describing the trailing boundary condition. It yields predictions that agree wel l with existing laboratory observations and more complex theoretical m odels of non-eroding, non-entraining, suspension-driven flows on horiz ontal surfaces. The essential features of gravity-surge behaviour have been observed and are captured accurately by the box model. These inc lude the increased rate of downstream loss of flow momentum with incre ased particle setting velocity, the existence of maxima in the thickne ss of proximal deposits, and the downstream thinning of distal deposit s. Our approximation for the final run-out distance, X(r), of a surge in deep water is given by X(r) approximate to 3(g'(o)q(o)(3)/W-s(2))(1 /5), where g'(o) is the initial reduced gravity of the surge, q(o) the initial two-dimensional volume, and W-s the average settling velocity of the particles in the suspension. A characteristic thickness of the resulting deposit is given by phi(o)q(o)/X(r), where phi(o) is the in itial volumetric fraction of sediment suspended in the surge. Our anal ysis provides additional insight into other features of gravity-surge dynamics and deposits, including the potential for the thickening of c urrents with time, the maintenance of inertial conditions and the pote ntial for strong feedback in the sorting of particle sizes in the down stream direction at travel distances approaching X(r). Box-model appro ximations for the evolution of gravity surges thus provide a useful st arting point for analyses of some naturally occurring turbidity surges and their deposits.